Bayes estimation of a distribution function using ranked set samples

作     者：Kvam, PH Tiwari, RC 

作者机构：Georgia Inst Technol Atlanta GA 30332 USA Univ N Carolina Dept Math Charlotte NC 28269 USA 

出 版 物：《ENVIRONMENTAL AND ECOLOGICAL STATISTICS》 (环境和生态统计学)

年 卷 期：1999年第6卷第1期

页      面：11-22页

核心收录：

学科分类：0830[工学-环境科学与工程（可授工学、理学、农学学位）] 08[工学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 

主　　题：Dirichlet distribution EM algorithm Gibbs sampler nonparametric estimation 

摘      要：Aranked set sample (RSS), if not balanced, is simply a sample of independent order statistics generated from the same underlying distribution F. Kvam and Samaniego (1994) derived maximum likelihood estimates of F for a general RSS. In many applications, including some in the environmental sciences, prior information about F is available to supplement the data-based inference. In such cases, Bayes estimators should be considered for improved estimation. Bayes estimation (using the squared error loss function) of the unknown distribution function F is investigated with such samples. Additionally, the Bayes generalized maximum likelihood estimator (GMLE) is derived. An iterative scheme based on the EM Algorithm is used to produce the GMLE of F. For the case of squared error loss, simple solutions are uncommon, and a procedure to find the solution to the Bayes estimate using the Gibbs sampler is illustrated. The methods are illustrated with data from the Natural Environmental Research Council of Great Britain (1975), representing water discharge of floods on the Nidd River in Yorkshire, England.